On the birth of the LFIs: Some alternative histories (2015)(João Marcos, UFRN, BR)

The Logics of Formal Inconsistency (LFIs) were crafted with the intention of subsuming a large amount of logical systems developed in and around the Brazilian School of Paraconsistency, following the general intuition that the metatheoretical notion of consistency was to be internalized at the object-language level. Some side projects that soon appeared were concerned with distinguishing the notions of “contradiction” and “inconsistency”, investigating the interaction between the paraconsistent negation and the consistency connective, studying the propagation of consistency, uncovering paraconsistent logics that constituted maximal fragments of classical logic, finding out which LFIs had natural and useful many-valued semantics, and which such systems had natural modal semantics.

The story could have been very different (or pretty similar) had we concentrated on other aspects of the logical systems that would give origin to the LFIs. We could have for instance decided to study logical systems containing a paraconsistent negation and a bottom particle, or study logics with more than one negation (at least one of them being paraconsistent), or study logics with different "levels of trivialization", or study logics that "dualized" constructive logics, and so on. But in fact we chose to concentrate on logics that allowed for the proof of some appropriate form of derivability adjustment theorem, whereby consistent reasoning would be recoverable. What was to be gained, and what has been lost? This talk will comment on some of the mentioned alternatives, and their interrelations.